Suppose we perform a sequence of n operations on a data structure such that if some condition C(k) holds then the kth operation takes O(k) time, but otherwise it only takes O(1) time. For each condition C(k) listed below, determine the total time T(n) for the sequence of all n operations, and also the amortized time Tamortized(n) per each operation

a) If C(k) is "k is a power of 3" then T(n)-O(n4/) and Tamortized(n) O(n13).
b) If C(k) is "k is a multiple of 2" then T(n)-O(n) and Tamortized(n)=O (1).
c) If C(k) is "k is a perfect square" then T(n) O(n4/3) and Tamortized(n)=O(n13). O
d) If C(k) is "k is a multiple of 2" then T(n)=O(n2) and Tamortized(n)=O(n)

In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x, y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.